Benchmark case studies in structural design optimization using the force method

Abstract

A structural optimization algorithm is developed for truss and beam structures under stress-displacement or frequency constraints. The algorithm combines the mathematical programming based on the Sequential Quadratic Programming (SQP) technique and the finite element technique based on the Integrated Force Method. A new approach based on the single value decomposition technique has been developed to derive the compatibility matrix required in the force method. Benchmark case studies illustrate the procedure and allow the results obtained to be compared with those reported in the literature. It is shown that the computational effort required by the force method is significantly lower than that of the displacement method and in some cases such as structural optimization problems with multiple frequency constraints, the analysis procedure (force or displacement method) significantly affects the final optimum design and the structural optimization based on the force method may result in a lighter design.

Optimal Design of Truss Structures with Continuous Variables Using Colliding Bodies Optimization

“…These examples include four well-known space trusses and two planar bridge structures. The number of design variables for the first to fifth examples are 8,16,7,32,26, respectively and for the last example 4, 8 and 12 variables are used. Similarly, the number of Colliding Bodies or agents for these examples are considered as 30, 40, 40, 50, 40 and 20, respectively.…”

“…In this example, the first two natural frequencies of the structure are considered as the constraints (ω 1 = 4 HZ, ω 2 ≥ 6 HZ). This example has been solved by Konzelman [31] using a dual method (DM) and by Sedaghati [32] using the force method (FM). Gomes [28] has investigated the problem using the Particle Swarm Optimization.…”

Enhanced Versions of the CBO Algorithm

“…6 HZ. This example has been solved previously by Konzelman [35] using a dual method (DM) and by Sedaghati [36] using the force method (FM). Gomes [21] has investigated the problem using the Particle Swarm Optimization.…”

Sizing Optimization Of Truss Structures Under Frequency Constraints With Artificial Bee Colony Algorithm

“…This is a mere size optimization. This example has been solved by Sedaghati [19] using the force method (FM). Gomes [9] has investigated the problem using the Particle Swarm Optimization.…”